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# The operation delta is defined for all nonzero x and y b x

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The operation delta is defined for all nonzero x and y b x [#permalink]

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29 Jul 2007, 11:56
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The operation # is defined for all nonzero x and y by x#y = x + x/y. If a>0, then 1#(1#a) =

A. a
B. a+1
C. a/(a+1)
D. (a+2)/(a+1)
E. (2a+1)/(a+1)

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jan 2014, 05:03, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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29 Jul 2007, 13:53
(E) for me

o 1 delta a
= 1 + 1/a
= (a + 1)/a

o 1 delta (1 delta a)
= 1 delta ((a + 1)/a)
= 1 + 1/((a + 1)/a)
= 1 + a/(a+1)
= (2*a + 1) / (a + 1)
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30 Jul 2007, 23:39
1 delta a = 1 + 1/a
Let 1 delta a be x

Then 1 delta (1 delta a) = 1 delta x = 1 + 1/x. Subsitute in x, to give

1 + 1/(1+1/a) = 1 + a/(a+1) = a+1+a/(a+1) = 2a+1/(a+1)
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Re: The operation delta is defined for all nonzero x and y b x [#permalink]

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02 Jan 2014, 08:26
Can someone explain the math better on this one? Brunnel, do you mind?
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Re: The operation delta is defined for all nonzero x and y b x [#permalink]

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03 Jan 2014, 05:04
jeremyl3763 wrote:
Can someone explain the math better on this one? Brunnel, do you mind?

The operation # is defined for all nonzero x and y by x#y = x + x/y. If a>0, then 1#(1#a) =
A. a
B. a+1
C. a/(a+1)
D. (a+2)/(a+1)
E. (2a+1)/(a+1)

$$1#(1#a) = 1#(1+\frac{1}{a}) = 1#(\frac{a+1}{a})= 1+ \frac{1}{(\frac{a+1}{a})}=1+\frac{a}{a+1}=\frac{a+1+a}{a+1}=\frac{2a+1}{a+1}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html
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Kudos [?]: 85673 [0], given: 10242

Re: The operation delta is defined for all nonzero x and y b x [#permalink]

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03 Jan 2014, 05:04
Re: The operation delta is defined for all nonzero x and y b x   [#permalink] 03 Jan 2014, 05:04
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